Heat transfer in an evaporating thin liquid film moving slowly along the walls of an inclined microchannel

A theoretical study has been undertaken to determine the rate of heat transfer in a thin evaporating liquid film flowing along the walls of a microchannel under the combined action of surface tension and gravity. Analytical solutions of conservation equations, in both liquid and vapour phases, have been obtained, in considerations with coupled heat and mass transfer boundary conditions at the interface. It has been recognized that while the local Nusselt number is influenced solely by the liquid film thickness, the average Nusselt number depends both on liquid film thickness and a dimensionless number ρgsinθ  δ02/σ, as obtained from the scale of characteristic velocity for both gravity and surface tension.